A new online music service that has thrown open its virtual doors with a claim to be "the way we want to consume music in the future", has swiftly fallen foul of the music industry's licensing practices.

Spotify, created by two Swedish entrepreneurs, Daniel Ek and Martin Lorentzon, has already attracted tens of thousands of users who spread private invitations to their friends after hearing about the site through internet chat. This week the company peeled off the "private" label to allow anyone in the UK to sign up.

However, Spotify has been forced to remove thousands of tracks in a row over licensing. This has infuriated users and the software industry, which accused record and film companies of lobbying government instead of adapting to the 21st century.

An internet radio service where users choose tracks, or let the company choose them, Spotify is being tipped as the leader of a new generation of innovative online music programs. Based in London and Stockholm, it opened up its service here after being "bowled over" by the level of interest.

Rather than buying music, users can fill playlists with songs of their choosing or create "collaborative" playlists which have their own web address and so can be passed around and added to by others.

Users can pick from a huge catalogue of songs, listen to them for free over the internet and, like commercial radio, hear a few adverts along the way. The service has deals with top labels around Europe, and claims to be doubling in size every few weeks. Dedicated users can also choose to buy a day's worth of ad-free access for 99p, or become a premium subscriber – where there are no adverts at all – for £10 a month.

But last month the Spotify catalogue shrank overnight by thousands of songs. The site's global community manager, Andres Sehr, wrote a blog post to say this was required by the record labels, which have strict rules about what can be played where.

"These restrictions are a legacy from when most music was sold on tapes and CDs and they have continued over into streaming music," Sehr said, adding, "our hope is that one day restrictions like this will disappear for good."

The cuts brought howls of dismay from users, while yesterday John Lovelock, chief executive of the Federation Against Software Theft and Investors in Software (FAS IiS), said: "Over the past decade the software industry has evolved to become more user-focused and more adaptable to changing market conditions." By contrast, he said, the entertainment industry had been pushing for more restrictions instead of adapting. "The entertainment sector appear to have lobbied the government to consider establishing a 'pirates tax' on all of us, as well as yet another quango to oversee it, meaning more cost and more hassle. It's time these industries came up to speed in the modern market and changed their business models to encourage their customers to use the internet for their purchasing."

Spotify does not yet offer links to let people buy tracks. That could come. For now, the co-founders are putting their own money into the company. "We had the idea in 2002, but realised that the timing might not be right so we waited until 2006," Ek said. "We're adding tens of thousands of users every day now, so it's growing quickly."

The company was founded in 2006 by Ek and Lorentzon, two established internet entrepreneurs who claim to have pumped in more than €8m (£7m) themselves. Despite the rocky economy, it already has more than 60 employees and received a €15m injection from two Scandinavian investment companies last year.

"We're not in it for the money," Ek said. "We do believe there's a very good business opportunity underlying here, but we did this because this is the way we want to consume music in the future."

Digital music is dominated by Apple, which uses its iTunes store as a way to convince people to buy iPods. But streaming services such as Last.fm in London, bought by the American media conglomerate CBS for $280m (£190m) in 2007, are growing in popularity. Last.fm's co-founder, Martin Stiksel, said: "There's definitely not such a consolidation as there was in online video streaming, where YouTube basically blew everyone away. There's still all these different business models out there … the jury's still out on the business of online music that's not connected with hardware."

One of Spotify's appeals is that it makes instantly listening to music easier than downloading it illegally. Online piracy and illegal filesharing has been a thorn in the side of the music business since the original Napster blew the industry apart in 1999. Many in the record industry still believe the majority of music that people acquire online comes via pirate networks.

Other, unlicensed services have generated buzz – but ultimately failed to blossom under intense legal pressure. Muxtape, an online mixtape creator from New York, was an underground hit last year but was forced to close after problems with the record labels it was negotiating with.

Although Spotify users cannot keep the tracks they hear, there are no restrictions on how many times they can listen to one track – meaning those who listen on their computer have less of an incentive to download illegally. In the future, the company hopes to provide a service that works on mobile phones, car stereos and even iPods.

"The ones we want to steal users from are the piracy services, that's our biggest competitor," said Ek. "This idea could be applied to other media as well. Who knows, in the future, Spotify could be something that works for movies, games or a lot of different things."